PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
975120^39131+9350911Lelio R Paula01/2013
9752(21*27^35567-94921)/2650910Curtis Bright05/2015
9753(7*2^169124-1)/954950909Lelio R Paula01/2014
9754(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
975513693^5212+5212^1369350897Hans Havermann02/2016
97567*5^72813+650895Lelio R Paula09/2014
97575*10^50890-8150891Robert Price04/2017
97583^106656-1202850888Enzo Doria02/2013
9759(2^169028+3)/25950881Lelio R Paula01/2012
97602^169000-112750875Yves Minet05/2013
976119^39780+1650869Lelio R Paula01/2013
9762(19*2^168960+1)/550863Lelio R Paula07/2012
9763(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
976511^48840+4650862Lelio R Paula01/2013
9764(5*10^50861-107)/350862Robert Price01/2017
976620^39087-420350854Enzo Doria03/2013
9767(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
97682^168907-54444750847Paul Bourdelais11/2012
976919312^429+429^1931250839Anatoly F. Selevich12/2006
97705^72716-1322650827Enzo Doria02/2013
97712^168823+102550821Lelio R Paula01/2009
97727*10^50818-8950819Robert Price01/2017
97742^168811+15015*16881150818Henri Lifchitz02/2005
97732^168813-283350818Yves Minet09/2014
9775(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
97767022^13211-13211^702250816Norbert Schneider12/2017
97772^168795+538550813Lelio R Paula05/2009
97787670^13079-13079^767050810Norbert Schneider09/2017
97794*3^106483+550806Lelio R Paula03/2014
978013^45606+450803Lelio R Paula01/2013
978113^45606-3850803Lelio R Paula01/2013
97822^168746+5890550798Lelio R Paula05/2009
9783(16*10^50795-43)/950796Robert Price02/2015
9784gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
97857*10^50789-4750790Robert Price02/2017
97862^168717-72952350789Paul Bourdelais11/2012
9787(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9788(21*2^168652-1)/21550769Lelio R Paula01/2014
97892^168629+1290950763Lelio R Paula01/2011
97909328^12787+12787^932850762Norbert Schneider01/2016
97912^168627+7311350762Enzo Doria04/2016
97922^168623+4733350761Yves Minet02/2010
9793(8*10^50750-101)/350751Robert Price10/2017
9794(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9795(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
97963*10^50727-3150728Robert Price10/2017
97976152^13387-13387^615250724Norbert Schneider03/2018
97988544^12901-12901^854450723Norbert Schneider05/2017
9799(17^41221+1)/1850720Paul Bourdelais03/2010
980010^50711+750712Jason Earls12/2007
980110^50711-31796950711Patrick De Geest04/2009
9802(17^41213+3^41213)/2050710Robert Price08/2013
9803(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
980447779!4+102450708Robert Price08/2017
98062^168431-15950703Lelio R Paula01/2011
9805(7*10^50702-1)/350703Erik Branger03/2014
9807117216#-p(117216)50700Henri Lifchitz03/2007
9808(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9809(13*2^168352-1)/47750678Lelio R Paula01/2014
98108*10^50675+3950676Robert Price01/2017
9811(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
981214415^3274+3274^1441550670Hans Havermann05/2016
9813(12379^12379+282)/1750663Makoto Morimoto07/2016
98155^72480-1712650662Enzo Doria02/2013
9814(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
98163^106143+250644Mike Oakes11/2009
98179178^12777-12777^917850633Norbert Schneider02/2017
9818(2*10^50603-41)/350603Robert Price01/2017
9819(12^46889-1)/1150601Paul Bourdelais09/2008
98202^168068-189350594Yves Minet09/2012
98212^168057+841550591Lelio R Paula11/2011
98224*10^50579+950580Robert Price05/2015
98232^168019-9439550579Lelio R Paula07/2011
98252^168019+7421350579Enzo Doria04/2016
9824(47*10^50578+493)/950579Robert Price11/2017
98265925^13406-13406^592550577Norbert Schneider03/2018
98273^106002+7050576Lelio R Paula07/2012
98285*2^167970-950565Lelio R Paula02/2014
9829(58*10^50558-13)/950559Robert Price09/2015
983088*10^50547+750549Robert Price11/2016
98312^167910-11262550546Enzo Doria06/2014
9832(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
98332^167866+1171550533Lelio R Paula05/2009
9834gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
98352^167847-13550527Lelio R Paula01/2011
9836-lucasV(-1,2,335684)50526Mike Oakes01/2017
9837(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9838(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
98402^167807+7550515Lelio R Paula08/2010
98392^167805+7627750515Enzo Doria04/2016
98418335^12882+12882^833550510Norbert Schneider03/2016
98427*2^167777+950507Lelio R Paula02/2014
984314162^3681+3681^1416250502Hans Havermann05/2016
9844(17*10^50495-11)/350496Robert Price07/2015
98452^167682+8550478Lelio R Paula08/2010
98462^167667-92742750473Paul Bourdelais11/2012
98479737^12654+12654^973750470Norbert Schneider01/2016
9848(9179*2^167644-1)/1750469Lelio R Paula03/2015
984913386^5891+5891^1338650468Hans Havermann05/2016
9850(10^50467-97)/350467Robert Kinser10/2017
9851(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
9852152^23124+15150453Eric Chen04/2018
98535003^13637-15650447Enzo Doria07/2012
98546^64826-2672350445Enzo Doria03/2013
9855(3^105718+7)/3250439Lelio R Paula03/2012
9856(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
985717^40989+5650435Lelio R Paula01/2013
9858(12329^12329+1652)/42150435Makoto Morimoto07/2016
98592*5^72153+750434Lelio R Paula09/2014
9860(3126^14431-1)/312550433Richard Fischer03/2015
98618078^12907-12907^807850432Norbert Schneider05/2017
986239^31694+3850428Norbert Schneider05/2014
9863(7*10^50414-151)/950414Robert Price09/2017
98642^167460+218750411Lelio R Paula11/2011
9865(12323^12323+2709)/2^450409Makoto Morimoto07/2016
986611^48400-771050404Enzo Doria02/2013
98672^167432+5461550403Lelio R Paula05/2009
9868(23*2^167430-1)/416950400Lelio R Paula01/2014
986968677!6-250395Robert Price07/2017
987019^39404+2250389Lelio R Paula01/2013
9871(102^25087-1)/10150388Richard Fischer08/2017
987235^32629-783450382Enzo Doria03/2013
98736^64744+16350381Lelio R Paula06/2012
9874116447#+17465950381Nicolas PALAU09/2016
98762^167353+12950379Lelio R Paula05/2009
987520^38722-113350379Enzo Doria03/2013
98783^105567-1650369Lelio R Paula07/2012
98772^167321-11284950369Enzo Doria06/2014
9879(28*10^50362-43)/350363Robert Price04/2016
988011421^12410-12410^1142150357Norbert Schneider08/2013
98812^167278-206350356Yves Minet03/2013
9882181^22300+22300^18150347Serge Batalov05/2014
98839932^12595-12595^993250343Norbert Schneider12/2016
98848993^12732-12732^899350342Norbert Schneider02/2017
98853*5^72018-450339Lelio R Paula09/2014
98862^167207-11268750335Enzo Doria06/2014
98876^64674-3750327Lelio R Paula06/2012
98882^167177+7480150326Enzo Doria04/2016
988913739^4600+4600^1373950323Hans Havermann10/2015
989011508^12391+12391^1150850320Norbert Schneider06/2014
98912^167132-216350312Yves Minet08/2013
98927^59527-6250307Lelio R Paula06/2012
9894(310027^9161+1)/31002850302Faysal YAtim04/2008
9893(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
98952^167083-11251950297Enzo Doria06/2014
9896272^20659-20659^27250296Norbert Schneider09/2015
989725337!!-1650290Robert Price06/2015
98989722^12611-12611^972250290Norbert Schneider12/2016
9899(15*2^167013+1)/64950275Lelio R Paula07/2012
990019^39315-1250275Lelio R Paula01/2013
99015^71925-3650274Lelio R Paula06/2012
99022^167002+279913950273Enzo Doria04/2016
990310957^12444-12444^1095750270Norbert Schneider07/2013
99048*10^50253-9950254Robert Price02/2017
99065^71894-5450252Lelio R Paula06/2012
9905(127^23887+1)/12850252Richard Fischer04/2017
990718^40028-550247Lelio R Paula01/2013
9908(3*2^166904+1)/127950241Lelio R Paula07/2012
99092^166888-7855750239Jorge Menendez02/2018
991024^36397+2350236Norbert Schneider12/2013
99117984*29^34345+2150230Curtis Bright05/2015
99123^105248-1352850217Enzo Doria02/2013
99136^64532-6550216Lelio R Paula06/2012
99145^71834-2061650210Enzo Doria03/2013
9915(31*2^166778-1)/365150204Lelio R Paula01/2014
99162^166752-11239750198Enzo Doria06/2014
9917(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
991811^48199-93050195Enzo Doria11/2012
99193*10^50194-750195Erik Branger11/2013
99209992^12549+12549^999250192Norbert Schneider10/2015
99212^166708+15750185Lelio R Paula01/2011
9922(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
99237*2^166685+350179Lelio R Paula02/2014
9924(104^24877+1)/10550176Richard Fischer02/2018
99257*2^166671-950174Lelio R Paula02/2014
99269*2^166670+750174Lelio R Paula02/2014
99272^166670-11254150173Enzo Doria06/2014
99286149^13242-13242^614950172Norbert Schneider01/2018
99292^166657+46550169Lelio R Paula11/2011
993017^40768-2050163Lelio R Paula01/2013
99322^166596-7879550151Lelio R Paula07/2011
9931135^23541+13450151Norbert Schneider04/2015
993324^36335-67350150Enzo Doria03/2013
9934(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9935(52*10^50149+119)/950150Robert Price10/2017
9936(28*10^50147-97)/350148Robert Price07/2016
9937263^20718-20718^26350137Norbert Schneider09/2015
9938t(167020)50133Robert Price01/2015
9939(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
99402868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
994112^46445-1950123Lelio R Paula12/2012
99422^166501-1459350122Enzo Doria04/2013
9943(31*2^166509-1)/368407750120Lelio R Paula01/2014
99442^166483-16950117Lelio R Paula01/2011
9945(188^22037+1)/18950114Eric Chen09/2017
99469^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9947(23*2^166487-1)/3377049950112Lelio R Paula01/2014
99482*5^71689-950109Lelio R Paula09/2014
994913495^5154+5154^1349550096Hans Havermann04/2016
99516^64369-11950089Lelio R Paula06/2012
99509224^12633-12633^922450089Norbert Schneider12/2016
99522^166370-11254150083Enzo Doria06/2014
9953(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
99542^166339-11232150074Enzo Doria06/2014
99555^71637-2250073Lelio R Paula06/2012
9956Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
9957(4*10^50060+137)/350061Robert Price07/2017
99585^71618-1382650059Enzo Doria02/2013
995915^42563-250058Lelio R Paula11/2012
99601943^15222+15222^194350058Serge Batalov05/2014
9961183^22125-250057Lelio R Paula10/2017
996211641^12310+12310^1164150053Norbert Schneider04/2014
996313537!-2^13537+150052Joe McLean06/2006
99642^166227-16446750040Gary Barnes08/2009
996512241^12241+475650039Makoto Morimoto07/2016
9966(106*10^50035-1)/350037Serge Batalov12/2014
996711^48044-81050033Enzo Doria11/2012
996815^42539+8850030Lelio R Paula11/2012
9969524^18397-523^1839750028Jean-Louis Charton10/2009
99702^166159-1449750019Enzo Doria04/2013
99712^166155+8785550018Lelio R Paula01/2009
99732^166138-1165550013Lelio R Paula07/2011
9972(L(239313)-1)/5-2^955150013Jorge Menendez06/2017
99746487^13118-13118^648750007Norbert Schneider10/2017
9975(16*10^50005+41)/350006Robert Price10/2017
99802^166104-11262550003Enzo Doria06/2014
9976(L(239265)-1)/5-2^90650003Jorge Menendez03/2017
9977(L(239265)-1)/5-2^315250003Jorge Menendez04/2017
9978(L(239265)-1)/5-2^2015550003Jorge Menendez04/2017
9979(L(239265)-1)/5-2^7891250003Jorge Menendez04/2017
99812^166100+19901550002Lelio R Paula05/2008
998710^50000+6585950001Milton L. Brown02/2006
9982(598*10^49999-31)/950001Robert Price02/2017
998310^50000+581092721613350001Jorge Menendez09/2017
998410^50000+581092760537750001Jorge Menendez09/2017
998510^50000+581092765837950001Jorge Menendez09/2017
998610^50000+581092767222350001Jorge Menendez09/2017
998810^49999+9170150000Patrick De Geest03/2005
998910^50000-19430350000Patrick De Geest02/2009
9990(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9991(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9992(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9993(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9994(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9995(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9996(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9997(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9998(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9999(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
10000(2^6972593/10^381525)%10^5000050000Michael Vang05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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